Electroweakly Interacting Massive Particles (EWIMPs), in other words, new massive particles that are charged under the electroweak interaction of the Standard Model (SM), are often predicted in various new physics models. EWIMPs are probed at hadron collider experiments not only by observing their direct productions but also by measuring their quantum effects on Drell-Yan processes for SM lepton pair productions. Such effects are known to be enhanced especially when the di-lepton invariant mass of the final state is close to the EWIMP threshold, namely twice the EWIMP mass. In such a mass region, however, we have to carefully take non-perturbative effects into account, because the EWIMPs become non-relativistic and the prediction may be significantly affected by e.g., bound states of the EWIMPs caused by the electroweak interaction. We study such non-perturbative effects using the non-relativistic effective field theory of the EWIMPs, and found that those indeed affect the differential cross section of the Drell-Yan processes significantly, though the effects are smeared due to the finite energy resolution of the lepton measurement at the Large Hadron Collider experiment.
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